トポロジー火曜セミナー

過去の記録 ~02/04次回の予定今後の予定 02/05~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
担当者 河野 俊丈, 河澄 響矢, 北山 貴裕, 逆井卓也
セミナーURL http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html
備考 Tea: 16:30 - 17:00 コモンルーム

2022年05月10日(火)

17:00-18:00   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
今野 北斗 氏 (東京大学大学院数理科学研究科)
Nielsen realization, knots, and Seiberg-Witten (Floer) homotopy theory (JAPANESE)
[ 講演概要 ]
I will discuss two different kinds of applications of Seiberg-Witten (Floer) homotopy theory involving involutions. The first application is about the Nielsen realization problem, which asks whether a given finite subgroup of the mapping class group of a manifold lifts to a subgroup of the diffeomorphism group. Although every finite subgroup is known to lift in dimension 2, there are manifolds of dimension greater than 2 for which the Nielsen realization fails. However, only few examples have been known in dimension 4. I will show that "4-dimensional Dehn twists" yield a large class of new examples. The second application is about 4-dimensional invariants of knots. I will introduce a version of "Floer K-theory for knots", and will explain that this framework gives the first comparison result for the smooth and topological versions of a certain knot invariant, called stabilizing number. Although the above two topics (Nielsen realization and knots) may seem to have different flavors, they are derived from a common idea. The first one is proved using a constraint on smooth involutions on a closed 4-manifold from Seiberg-Witten homotopy theory by Yuya Kato, and the second one is derived from a generalization of Kato's result to 4-manifolds with boundary using Seiberg-Witten Floer homotopy theory. This talk is partially based on joint work with Jin Miyazawa and Masaki Taniguchi.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html